Propellant slosh is a potential source of disturbance critical to the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. Our previous effort has demonstrated the soundness of a CFD approach in modeling the detailed fluid dynamics of tank slosh and the excellent accuracy in extracting mechanical properties (slosh natural frequency, slosh mass, and slosh mass center coordinates). For a practical partially-filled smooth wall propellant tank with a diameter of 1 meter, the damping ratio is as low as 0.0005 (or 0.05%). To accurately predict this very low damping value is a challenge for any CFD tool, as one must resolve a thin boundary layer near the wall and must minimize numerical damping. This work extends our previous effort to extract this challenging parameter from first principles: slosh damping for smooth wall and for ring baffle. First the experimental data correlated into the industry standard for smooth wall were used as the baseline validation. It is demonstrated that with proper grid resolution, CFD can indeed accurately predict low damping values from smooth walls for different tank sizes. The damping due to ring baffles at different depths from the free surface and for different sizes of tank was then simulated, and fairly good agreement with experimental correlation was observed. The study demonstrates that CFD technology can be applied to the design of future propellant tanks with complex configurations and with smooth walls or multiple baffles, where previous experimental data is not available.